Airports across the UK have stepped up security after a burning car was driven into a terminal building in Glasgow.
Police closed off roads around Liverpool's John Lennon Airport
Liverpool's John Lennon Airport was closed for more than eight hours as police removed a suspicious vehicle.
Other airports have closed roads outside terminal buildings and armed police patrols have increased.
Glasgow Airport re-opened to arrivals when a plane from Ibiza touched down at 0737 BST but aircraft will not start flying out of the airport until later.
On Saturday night, some 2,300 stranded passengers were taken to a reception area in the city centre.
BAA, which operates the airport, said staff had worked through the night to try to ensure a swift return to normal operations.
Spokesman Malcolm Robertson said: "Our advice to passengers is do not travel to the airport unless your airline has specifically confirmed your flight is going."
A number of Sunday morning flights have been cancelled at John Lennon Airport, which was closed at about 2030 BST on Saturday.
Between 400 and 500 passengers were taken by shuttle bus to two leisure centres in the city where the Salvation Army and council workers provided food, blankets and medical aid.
The airport was re-opened at about 0440 BST on Sunday.
In a statement, Merseyside Police said: "A vehicle has been removed from the airport and taken away for forensic testing.
"Customers hoping to use the airport are advised that they should contact their airline to confirm whether their flight will be going ahead. All cordons around the airport have now been lifted."
More armed police
Some flights which were due to land in Liverpool were diverted to East Midlands Airport.
A spokeswoman for East Midlands said extra security staff and armed police had been drafted in but otherwise the airport was running a normal service.
Thousands of passengers were stranded in Glasgow
Following the attack in Glasgow and the discovery of two car bombs in London on Friday, the government has raised the UK's terrorism threat level to "critical" - which means an attack is expected imminently.
BAA, which runs several major airports including Heathrow, Gatwick, Stansted and Edinburgh in addition to Glasgow, said it had increased security.
Dropping off and picking-up passengers in front of the airports has been severely restricted and there may be significant delays in reaching the terminal by car, the operator warned.
It said passengers should try to reach airports via public transport to avoid delays.
Security measures include:
- Increased armed patrols at many airports including Heathrow and London City
- The road outside Birmingham International Airport is closed and traffic is being diverted to the short-stay car park
- Extra police patrols are in place at Manchester Airport and Blackpool Airports where cars are not being allowed to drive to the front of the terminals
- Taxi ranks at Luton Airport have been moved away from the terminal to stop cars approaching
In London, police said they would be making more use of stop and search under the Terrorism Act and there would be patrols by armed response vehicles around mainline train stations.
A spokesman for Transport for London (TfL), which runs the Tube system, said it had been informed that the general threat level to the UK had been raised to critical.
"The current threat level to the London transport system remains unchanged and we have no information of a specific threat against the TfL network.
"We will be drawing on long-standing procedures to deal with the heightened alert status."
The Metropolitan Police force has also reviewed security surrounding the memorial concert for Diana, Princess of Wales, at Wembley.
Those going should allow extra time because increased searches are likely to be taking place, a spokesman said.